PERCENTAGE

A percentage is a way of expressing a number or ratio as a fraction of 100. The term "percent" means "per hundred" or "out of 100." It is a way to describe a part or portion of a whole in terms of a fraction where the denominator is always 100.

For instance, if you have 25 apples out of 100, it can be expressed as 25%. In other words, 25% of the total number of apples is 25. The "%" sign represents a proportion out of 100.

Percentages are commonly used in various fields such as mathematics, finance, statistics, and everyday life. They are used to represent proportions, changes, discounts, interest rates, and many other concepts involving parts of a whole. Understanding percentages is essential for interpreting data, making comparisons, and analyzing information in different contexts

Percentage is a way of expressing a fraction or ratio in terms of parts per hundred.
The symbol for percentage is "%", which means "out of 100"

Calculating Percentages:

Calculating percentages involves finding a proportion or share of a whole amount represented by a fraction of 100. Here are some common scenarios and their corresponding methods for calculating percentages:

Mathematical definition of Percentage:

The mathematical definition of a percentage is a fraction or ratio expressed as a portion of 100. It's a way of representing a part of a whole in relation to the entire quantity, with the whole being represented as 100%.

Mathematically, a percentage is denoted using the "%" symbol. If $p$ represents a percentage, it is written as $p %$ and is equal to $p$ as a fraction.

For example, if you have 30% of a total quantity, it means you have (

30/100

or 0.3 times the whole quantity. Conversely, converting a decimal or a fraction to a percentage involves multiplying by 100

Tips and Formulas for Percentage

Understanding percentages allows for easy comparisons, analyses, and representations of parts of a whole, making it a fundamental concept in various mathematical calculations, finance, statistics, and everyday situations

Practice Questions on Percentages

1.The average of 5 numbers is 25. If one number is excluded, the average becomes 20. What is the excluded number?

A. 25
B. 30
C. 35
D. 40

Answer (C)

Let the excluded number be $x$ . The total sum of the 5 numbers = $5 \times 25 = 125$ After excluding $x$ , the total sum of 4 numbers = $4 \times 20 = 80$

The excluded number $x = 125 - 80 = 45$ . Therefore, the excluded number is 45 (Option: C)

2.The average of 7 numbers is 12. If one number is excluded, the average becomes 11. What is the excluded number?

A. 5
B. 6
C. 7
D.18

Answer (D)

Let the excluded number be $y$ . The total sum of the 7 numbers = $7 \times 12 = 84$ After excluding $y$ , the total sum of 6 numbers = $6 \times 11 = 66$

The excluded number $y = 84 - 66 = 18$ . Therefore, the excluded number is 18

3.The average of 9 numbers is 15. If one number is excluded, the average becomes 14. What is the excluded number?

A. 23
B. 24
C. 25
D. 26

Answer (A)

Let the excluded number be $z$ . The total sum of the 9 numbers = $9 \times 15 = 135$ After excluding $z$ , the total sum of 8 numbers = $8 \times 14 = 112$

The excluded number $z = 135 - 112 = 23$ . Therefore, the excluded number is 23

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PERCENTAGE

PERCENTAGE

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